represents a Gaussian white noise process with mean 0 and standard deviation 1.


represents a Gaussian white noise process with mean 0 and standard deviation σ.


represents a white noise process based on the distribution dist.



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Basic Examples  (1)

Define a Gaussian white noise process:

Simulate the process:

Mean and variance functions:

Covariance function:

Scope  (2)

Simulate a white noise process having normal slices with standard deviation 5:

Uniform distribution slices:

Discrete uniform distribution slices:

Process parameter estimation:

Estimate the process parameters from sample data:

Applications  (2)

Add white noise to a periodic signal:

Define a moving-average process:

Simulate the process:

Mean, variance, and kurtosis for the process:

Compare with the property values for the corresponding MAProcess:

Properties & Relations  (6)

WhiteNoiseProcess is a discrete-time process:

The states may either be continuous or discrete:

SliceDistribution[WhiteNoiseProcess[dist],t] is equal to dist:

Multivariate slices are products of dist with itself:

The slice mean is always zero:

WhiteNoiseProcess is uncorrelated according to the AutocorrelationTest:

Gaussian white noise is a special case of an MAProcess:

Compare covariance functions:

Possible Issues  (1)

EstimatedProcess fails for this example involving white noise from a uniform distribution:

Using a symmetric interval for UniformDistribution helps in this case:

Neat Examples  (1)

A family of white noise processes:

Introduced in 2014